In general, a fully-closed loop position controller used for shaft control of a numerically-controlled machine controls a load position θL of a controlled objective (hereinafter referred to as “target plant”) in accordance with a position command value XC supplied from a higher-level device by controlling a control input τm to a drive motor. Thus, a fully-closed loop position controller requires a high level of system stability (including a vibration suppression performance), an accurate command following performance, and a high level of load disturbance suppression performance.
FIG. 5 is a block diagram showing an example of a conventional fully-closed loop position controller. The target plant 200 is represented in terms of a rotational motor shaft. As the target plant 200 has a transfer pole ωP and a transfer zero ωZ as transfer characteristics, the target plant 200 is described in a configuration in which a motor moment of inertia Im and a load moment of inertia IL are connected via a spring system having a rigidity K. “s” represents an operator of a Laplace transform. An equation of motion of the target plant 200 is represented by the following Equation (1):
                              τ          m                =                                                            I                m                            ⁢                                                d                  ⁢                                                                          ⁢                                      ω                    m                                                  dt                                      +                          K              ⁡                              (                                                      θ                    m                                    -                                      θ                    L                                                  )                                              =                                                    I                m                            ⁢                                                d                  ⁢                                                                          ⁢                                      ω                    m                                                  dt                                      +                                          I                L                            ⁢                                                d                  ⁢                                                                          ⁢                                      ω                    L                                                  dt                                      +                          τ              d                                                          Equation        ⁢                                  ⁢                  (          1          )                    where ωm is a motor velocity, θm is a motor position, ωL is a load velocity, and τd is a load disturbance torque.
A conventional fully-closed loop position controller 300 in FIG. 5 is described below. A subtractor 50 subtracts a load position θL sensed by a load position sensor (not shown) from a position command value XC supplied from a higher-level device (not shown). A position deviation which is an output from the subtractor 50 is amplified by position loop gain KP times by a position deviation amplifier 51 to be used as a velocity command value. A subtractor 52 subtracts a mixed velocity feedback ωfb from the velocity command value. The velocity deviation which is an output from the subtractor 52 is amplified by velocity loop gain GV times by a velocity deviation amplifier 53 to be used as a control input τm to a drive motor.
The velocity loop gain GV can be obtained based on a proportional gain GP and an integral gain Gi from the following Equation (2):GV=GP+Gi/s  Equation (2)
As the velocity loop gain GV does not specify a velocity control band, the natural resonance frequency ωv of the velocity control system with a rigid body approximation applied to the target plant 200 is assumed to be the velocity control band so as to associate the velocity control band ωv with the proportional gain GP and the integral gain Gi by the following Equation (3).GP=2(Im+IL)ωv, Gi=(Im+IL)ωv2  Equation (3)
A differentiator 57 outputs a load velocity ωL by applying a temporal differentiation to the load position θL. A motor velocity tom is sensed by a sensor (not shown) such as a position sensor and a velocity sensor disposed at the motor. A subtractor 56 subtracts the motor velocity tom from the load velocity ωL. Then, the output of the subtractor 56 is amplified by mix gain fb times by an amplifier 55, and added with the motor velocity ωm by an adder 54 to be used as a mixed velocity feedback ωfb. This process is defined by the following Equation (4):ωfb=(1−fb)ωm+fbωL  Equation (4)where the mix gain fb represents a mix ratio of the motor velocity tom and the load velocity ωL in the mixed velocity feedback ωfb. The mix gain fb is a parameter which is set in a range of 0≤fb<1.
Next, a stability limit of the position control system shown in FIG. 5 is described. Because the effect of the integral gain Gi to the stability issue is limited, the gain Gi is assumed to be zero (Gi=0). The following equation can be obtained by calculating the stability limit of the fully-closed loop position control based on the well-known Routh stability criterion:
                                          K            p                    ⁢                      ω            v                          <                              {                                          R                -                                                      (                                          1                      +                      R                                        )                                    ⁢                                      f                    b                                                                              2                ⁢                                  (                                      1                    +                    R                                    )                                ⁢                                                      (                                          1                      -                                              f                        b                                                              )                                    2                                                      }                    ⁢                      ω            z            2                                              Equation        ⁢                                  ⁢                  (          5          )                    where the ratio of load moment of inertia R=IL/Im, and the zero angular frequency of the target plant ωz=(K/IL)1/2.
Equation (5) indicates that the vibration characteristics become significant unless the servo gain (Kpωv) is reduced, because increase in the load moment of inertia IL decreases the zero angular frequency ωz, resulting in a smaller right side of the equation. However, it is known that the vibration suppression performance can be improved by setting the mix gain fb because the stability limit can be increased, in particular when the ratio of load moment of inertia R is high.
Thus, a stability limit increase ratio h(fb) is defined by using the mix gain fb in the following Equation (6):
                              h          ⁡                      (                          f              b                        )                          =                                            R              -                                                (                                      1                    +                    R                                    )                                ⁢                                  f                  b                                                                                    (                                  1                  +                  R                                )                            ⁢                                                (                                      1                    -                                          f                      b                                                        )                                2                                                          R                          1              +              R                                                          Equation        ⁢                                  ⁢                  (          6          )                    
FIG. 6 is a graph showing the stability limit increase ratio h(fb) against the mix gain fb with the ratio of load moment of inertia R used as a parameter. Equation (6) represents that the stability limit increase ratio h(fb) reaches the maximum with fb=(R−1)/(1+R). When the mix gain fb over this value is set, h(fb) rapidly decreases and easily enters into the range of h(fb)<1, as shown in FIG. 6.
In other words, for a control shaft having a significantly changing ratio of load moment of inertia R, it is required to select an optimum mix gain fb at the minimum R(Rmin) and set a sufficient servo gain (Kpωv) in consideration of the stability limit at the maximum R(Rmax).
Next, as an example, a target plant having the ratio of load moment of inertia R changing in the range of 3≤R≤10 is discussed. The servo gain (Kpωv) can be obtained from the following Equation (7), which applies a margin constant β (0.4<β<0.6) to Equation (5) in consideration of the stability limit and the vibration suppression characteristics:
                                          K            p                    ⁢                      ω            v                          =                              β            ⁢                          {                                                R                  -                                                            (                                              1                        +                        R                                            )                                        ⁢                                          f                      b                                                                                        2                  ⁢                                      (                                          1                      +                      R                                        )                                    ⁢                                                            (                                              1                        -                                                  f                          b                                                                    )                                        2                                                              }                        ⁢                          ω              z              2                                =                      β            ⁢                          {                                                R                  -                                                            (                                              1                        +                        R                                            )                                        ⁢                                          f                      b                                                                                        2                  ⁢                                      (                                          1                      +                      R                                        )                                    ⁢                                                            (                                              1                        -                                                  f                          b                                                                    )                                        2                                                              }                        ⁢                          K                              R                ·                                  I                  m                                                                                        Equation        ⁢                                  ⁢                  (          7          )                    
Frequency characteristics of a command response θL/XC and a disturbance response ωL/τd supplied from the position control system shown in FIG. 5 are described by assuming that the target plant has characteristics of ωZ=64 rad/s=10 Hz in the case of R=10.
FIG. 7 shows frequency characteristics, in particular, when the servo gain (the position loop gain Kp and the velocity control band ωv) is appropriately set based on Equation (7) in the case of mix gain fb=0. In contrast, FIG. 8 shows frequency characteristics when the servo gain (Kpωv) is appropriately set based on Equation (7) in the case of R=10 with the mix gain fb=0.5, which achieves the maximum stability limit increase rate h(fb) in the case of R=3.
In this example, the mix gain fb=0.5, which is an optimum mix gain in the case of R=3 with the ratio of load moment of inertia R in the range of 3≤R≤10. Therefore, based on FIG. 6, the stability limit increase rate h(fb) is about 1.8 in the case of R=10. Accordingly, the command following performance is improved with the cutoff frequency of the command response θL/Xc increased from 10 Hz to 15 Hz. In addition, the load disturbance suppression performance in a middle or low frequency range is also improved about −7 dB. However, because the maximum value of the stability limit increase rate h(fb) is about 3 in the case of R=10, the control performance is not improved to nearly a limit.
As a conventional art, JP 2013-148422 A can be raised as an example.
As described above, in a conventional fully-closed loop position controller in which the velocity control system is configured based on a mixed velocity feedback ωfb of the motor velocity ωm and the load velocity ωL, the control performance cannot be sufficiently improved by the mix velocity feedback, in particular for a control shaft with a significantly changing ratio of load moment of inertia R.